Related papers: Approximate Entropy Analysis for Nonlinear Beam Dy…
The motion of beams in particle accelerators is dominated by a plethora of non-linear effects which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting…
Approximate entropy (ApEn) has been widely used as an estimator of regularity in many scientific fields. It has proved to be a useful tool because of its ability to distinguish different system's dynamics when there is only available…
The understanding of non-linear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity the beam lifetime optimisation. A detailed analysis of the multidimensional phase space…
Nonlinear dynamics can impact the performance of a particle accelerator in a number of different ways, depending on the type of the accelerator and the parameter regime in which it operates. Effects can range from minor changes in beam…
Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the…
Conventional particle accelerators use linear focusing forces for transverse confinement. As a consequence of linearity, accelerating rings are sensitive to myriad resonances and instabilities. At high beam intensity, uncontrolled…
The investigation of single-particle dynamics in circular particle accelerators can be traced back to pioneering works in the 1950s. Traditionally, the design of new circular accelerators has focused on optimising linear dynamics, striving…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
Modern and future particle accelerators employ increasingly higher intensity and brighter beams of charged particles and become operationally limited by coherent beam instabilities. Usual methods to control the instabilities, such as…
The beam normal spin asymmetry for the elastic $eN$ scattering is studied in the leading logarithm approximation. We derive the expression for the asymmetry, which is valid for any scattering angles. The result is compared with the results…
Nonlinear optics is a promising idea potentially opening the path towards achieving super high beam intensities in circular accelerators. Creation of a tune spread reaching 50% of the betatron tune would provide strong Landau damping and…
In this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device…
Shannon entropy, as a chaos indicator, is used for online Poincar\'e map regularization and dynamic aperture optimization in the National Synchrotron Light Source-II (NSLS-II) ring. Although various chaos indicators are widely used in…
Beam tracking software for accelerators typically falls into two categories: fast envelope simulations limited to linear beam optics, and slower multiparticle simulations that can model nonlinear effects. To find a middle ground between…
In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
A data-driven chaos indicator concept is introduced to characterize the degree of chaos for nonlinear dynamical systems. The indicator is represented by the prediction accuracy of surrogate models established purely from data. It provides a…
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator…